CN116755148A - Orthogonal anisotropic medium multidirectional reflection wave travel time inversion method - Google Patents
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Abstract
The invention provides a multi-azimuth reflected wave travel time inversion method of an orthotropic medium, which comprises the following steps: step 1, establishing a global coordinate system and a local coordinate system; step 2, establishing an orthotropic medium single-azimuth reflection P wave travel time approximate formula under a local coordinate system; step 3, carrying out anisotropic parameter inversion of the orthotropic medium based on the local coordinate system of single-azimuth travel time; step 4, establishing an anisotropic parameter conversion formula under a global coordinate system; step 5, carrying out global anisotropic parameter inversion based on a conversion formula; and 6, performing inversion result precision evaluation. The orthogonal anisotropic medium multidirectional reflection wave travel time inversion method can more fully utilize multidirectional seismic data, provide richer anisotropic information, and lay a foundation for subsequent stratum attribute identification and geological interpretation work.
Description
Technical Field
The invention relates to the technical field of petroleum geophysical exploration, in particular to a multi-azimuth reflected wave travel time inversion method for an orthotropic medium.
Background
Anisotropy is widely present in subsurface media, which in seismic exploration is predominantly manifested as velocity anisotropy. The anisotropic causes of the underground medium are various, including the directional arrangement of crystal minerals, the fine layering of sedimentary rock, the directional arrangement of cracks, the influence of ground stress and the like. In shale oil and gas exploration and development, a channel and a reservoir space for controlling oil and gas migration by a crack are important identification marks of geological desserts; in the horizontal fracturing process, in order to ensure the fracturing effect, the direction of the maximum principal stress of the stratum level and the horizontal stress difference are required to be identified. Therefore, in the field of shale oil and gas exploration, research on azimuth anisotropy is increasingly paid attention to.
Anisotropic media with azimuthal anisotropy characteristics can be classified from simple to complex according to symmetry into horizontal transverse isotropic (Horizontal Transverse Isotropic, HTI) media, orthotropic media, monoclinic anisotropic media, and the like. Wherein when two sets of perpendicular cracks orthogonal to each other exist in the underground medium, the equivalent medium is an orthotropic medium. In the TI medium, since there is one symmetry axis, it is only necessary to determine the velocity in the direction of the symmetry axis and in the direction perpendicular to the direction of the symmetry axis and the gradient of the change in velocity in the plane of the axis parallel to the symmetry axis after determining the coordinate system from the symmetry axis. For orthotropic media, there are two planes of symmetry, so after determining the coordinate system from the planes of symmetry, it is necessary to determine the speed of propagation along the three axes and the gradient of the change in speed in the three axes.
Beginning in 1997, studies on orthotropic media have proposed the orthotropic media theory by Tsvakin and derived the P-wave velocity and related anisotropic parameters of the orthotropic media based on their elastic coefficient matrix. Subsequent studies on orthotropic media mainly include forward and inversion of reflected wave travel time and amplitude, etc. The travel time inversion is mainly based on NMO speed inversion, wherein the NMO speed is the speed used for correcting the normal time difference of the travel time of the reflection hyperbola. The NMO speed is regular along with the change of azimuth and is in an elliptical attribute, and the azimuth attribute of the anisotropic medium can be accurately determined by inverting the NMO speed. However, the inversion process of the NMO speed is more dependent on a priori information such as the thickness of the reflecting layer, the propagation speed in the vertical direction, and the like, and thus has a certain limitation.
In application number: in CN202010817813.5, a method and a system for inversion of orthotropic velocity are related, where the method includes: collecting integrated image point gathers and superposition data; performing cross-correlation calculation in a processing time window defined by a user by utilizing each seismic data channel in the model channel and the imaging point channel set; performing cross-correlation calculation on each cross-correlation time window of the current seismic data; processing all seismic data traces in the current imaging point trace set; calculating the HTI anisotropic speed parameters of the current imaging point gather on all zero offset data samples by using a weighted least square algorithm according to the residual time difference data, the correlation coefficient data and the prestack time migration speed field data of the current imaging point gather; obtaining a VTI anisotropic speed parameter according to the HTI anisotropic speed and the residual error part of the residual time difference; and processing each imaging point gather to obtain an orthotropic velocity inversion result of all the seismic data, wherein the method has high-efficiency calculation efficiency and high calculation result precision.
In application number: the patent application of CN201210371061.X relates to a full waveform inversion method and device for seismic anisotropy parameters, and belongs to the field of seismic anisotropy parameter prediction in petroleum geophysical exploration. The method comprises the following steps: (1) Acquiring seismic data to be subjected to anisotropic parameter inversion, namely observed wave field data; (2) Denoising the seismic data obtained in the step (1) to obtain denoised data; (3) Extracting a common center point gather according to coordinates of shot points and detection points by using the denoised data obtained in the step (2) to obtain seismic CMP gather data, and then calculating the layer speed of a horizontal stratum by using the seismic CMP gather data; (4) Constructing an initial model for inversion by interpolation by using the layer speed of the horizontal stratum obtained in the step (3); (5) And carrying out micro disturbance on each parameter of the initial model to generate a model after parameter disturbance.
In application number: in CN202011148799.0, a method, an apparatus, an electronic device, and a medium for calculating an orthotropic parameter are related. The orthotropic parameter calculation method comprises the following steps: extracting the residual time difference of the azimuth gather; inverting the anisotropic parameters of the HTI medium by using the residual time difference; performing time difference correction on the azimuth gather; the anisotropic parameters of the VTI medium are inverted using the amplitude. According to the method, from the azimuth prestack gather, HTI media and VTI media are respectively considered and are respectively inverted, so that the problem that inversion results are inaccurate due to mutual interference and mutual influence in conventional primary inversion is solved, and another road is opened for developing two groups of crack anisotropy prediction technologies which are stable and rapid and have high signal to noise ratios.
In application number: in CN201911059377.3, a method for inverting the fluid factor and fracture parameters of orthotropic media is disclosed. The method comprises the following steps: using a vertical and transverse isotropic medium in a dry rock background, and deducing a rigidity matrix of the orthosymmetric anisotropic fracture medium according to the fracture weakness; by utilizing the assumption of weak anisotropy and small crack weakness and combining an anisotropic Gassmann equation, a new expression of weak anisotropy approximate rigidity of saturated fluid rock in an orthogonal medium is derived; combining rigidity disturbance and scattering theory to obtain a PP wave linear reflection coefficient of decoupling of fluid and fracture parameters in the orthogonal symmetry weak anisotropic medium; and using logging information as priori information, and utilizing partial incidence angle superposition azimuth seismic data to realize elastic impedance pre-stack inversion along with the change of offset and azimuth under a Bayesian framework. The invention can provide reliable results for fluid identification and fracture characterization, and provides technical support for propagation research of seismic waves, oil gas development and seismic disaster prevention.
The prior art is greatly different from the invention, the technical problem which is needed to be solved by the invention is not solved, and the invention provides a novel orthogonal anisotropic medium multidirectional reflection wave travel time inversion method.
Disclosure of Invention
The invention aims to provide the orthogonal anisotropic medium multidirectional reflection wave travel time inversion method which can more fully utilize multidirectional seismic data and provide more abundant anisotropic information.
The aim of the invention can be achieved by the following technical measures: the method for inverting the orthogonal anisotropy medium multidirectional reflection wave travel time comprises the following steps:
step 1, establishing a global coordinate system and a local coordinate system;
step 2, establishing an orthotropic medium single-azimuth reflection P wave travel time approximate formula under a local coordinate system;
step 3, carrying out anisotropic parameter inversion of the orthotropic medium based on the local coordinate system of single-azimuth travel time;
step 4, establishing an anisotropic parameter conversion formula under a global coordinate system;
step 5, carrying out global anisotropic parameter inversion based on a conversion formula;
and 6, performing inversion result precision evaluation.
The aim of the invention can be achieved by the following technical measures:
in step 1, a Cartesian coordinate system is assumed as the global coordinate system, x 3 The axis being vertical, x 1 ，x 2 The axes being horizontal and mutually orthogonal, the axial plane (x 1 ，x 2 )、(x 1 ，x 3 ) Respectively parallel to two symmetrical planes of the medium; the background medium is a uniform stratum, the thickness of the stratum is H, the horizontal reflecting surface at the bottom of the stratum and (x) 1 ，x 2 ) Planes are parallel; in this case, the incident downstream and reflected upstream rays of the P-wave lie in a plane perpendicular to the reflecting surface and are symmetrical with respect to the normal to the reflecting surface.
In step 1, for a seismic observation system, a local coordinate system, reflected rays and two used coordinate system schematics are defined: global coordinate system x i And a local coordinate system x' i The method comprises the steps of carrying out a first treatment on the surface of the Corner angleIs the azimuth of the source detector profile, SO is the incident ray, and OR is the reflected ray.
In step 1, a seismic wave is excited from a seismic source S at the origin of a global coordinate system, reflected at a point O and transmitted to a detector R; the axes on which the points S and R lie are defined as x 'of the local coordinate system' 1 Axis, and x' 1 The axes being in the same horizontal plane and being x' 1 The axis perpendicular to the axis is x' 2 An axis perpendicular to x' 1 Axis, x' 2 The axis of the shaft is x' 3 A shaft; the origin of the local coordinate system coincides with the source S and also represents the global coordinate system x i Origin of (x) vertical axis x 3 The same is true in both local and global coordinate systems; the reflected rays lie in a local coordinate system (x' 1 ，x′ 3 ) In-plane, with a coordinate plane (x 1 ，x 3 ) Included angle
In step 2, in a two-dimensional coordinate system, the reflected wave travel time T has the following form:
wherein x is offset distance, namely distance between the seismic source S and the detector R, H is depth of the horizontal reflecting surface and coincides with the symmetry plane of the stratum; t=t (x) denotes the travel time of the reflected P wave; v=v (n) denotes group velocity, n being a phase vector; the widely used representation method in time difference analysis is utilized:
wherein ,for normalized offset, α is P in the reference isotropic mediumWave phase velocity, T 0 Double-pass time-shifting for reference zero offset; equation (1) is rewritten as:
in step 2, a phase velocity square approximation is used, i.e. v 2 (N)～c 2 (N) approximately represents group velocity v (N); in a two-dimensional coordinate system, the group velocity of an orthotropic medium can be expressed using an anisotropy parameter as:
in the formula (3), N is a velocity direction vector, which can be obtained byThe representation is made of a combination of a first and a second color,
the anisotropic parameters involved include epsilon x ，ε z ，η y, wherein ,εx ，ε z Respectively represent the medium in the coordinate axis x 1 、x 3 The difference between the direction P wave phase velocity and the reference velocity α; η (eta) y Representing the medium in a coordinate plane (x 1 ,x 3 ) A gradient of change in velocity of the internal P-wave; the anisotropic parameters in the local coordinate system are related to the stiffness coefficients in the local coordinate system:
wherein ,Aij Normalizing elements in the stiffness coefficient matrix for the density of the stratum medium under a local coordinate system, wherein alpha is the P wave phase speed in the reference isotropic medium;
simplified, equation (3) can be written in the form:
the step 3 comprises the following steps:
step 31, calculating ε based on zero offset travel time z ；
Step 32, constructing an inversion determinant;
step 33, solving the inversion determinant.
At step 31, at zero offset, i.e., x=0, formula (7) and formula (8) become:
therefore, the A parameter ε can be directly obtained by equation (12) z ：
In step 32, according to equation (10), equations (7) and (8) may be rewritten as:
the inversion determinant is constructed according to equation (11) as follows:
Gm＝d, (12)
wherein G is a coefficient matrix of n×m, N is the number of detectors, M is the number of a parameters involved, m=2 in this section; the row vectors in matrix G are of the form:
m consists of 2 parameters, which are in the form:
m＝(ε x ，η y ) T ， (14)
the form of vector d is as follows:
to normalize offset, T obs For the travel time received by the detector.
In step 33, equation (12) may be solved by least squares, and the inverted objective function is:
||Gm-d|| 2 ＜κ， (16)
wherein, κ is a parameter for controlling inversion accuracy; solving equation (16) by equation (17):
wherein ,for inversion operators
wherein ,GT The inversion process is more stable with larger epsilon, but lower accuracy, which is the transpose of matrix G, I is N identity matrix, epsilon is a stability factor.
In step 4, under the three-dimensional coordinate system, firstly, assume that the seismic lines distributed along different directions on a plane have a trend angle ofFrom the trend of the line x 1 The local coordinate system in the axial direction is converted into the global coordinate system, and the conversion matrix R is as follows:
distinguishing the orthotropic medium anisotropy parameters in the local coordinate system from the orthotropic medium anisotropy parameters in the global coordinate system using a superscript; according to the matrix transformation rule of 6 multiplied by 6 rigidity coefficient in Bond transformation, the anisotropic parameter epsilon 'of orthotropic medium in local coordinate system' x ，η′ y and ε′z The conversion to a global coordinate system can be achieved by the following formula:
ε′ z ＝ε z , (22)
the definition of the anisotropic parameters in the local coordinate system is shown in formula (6), and the global anisotropic parameters comprise epsilon x ，ε y ，ε z ，η x ，η y ，η z, wherein ,εx ，ε y ，ε z Respectively represent the medium in the coordinate axis x 1 、x 2 、x 3 The difference between the direction P wave phase velocity and the reference velocity α; η (eta) x ，η y ，η z Respectively representing the medium in a coordinate plane (x 2 ,x 3 )、(x 1 ,x 3 )、(x 1 ,x 2 ) A gradient of change in velocity of the internal P-wave; the anisotropic parameters in the global coordinate system are related to the stiffness coefficients in the global coordinate system:
wherein ,Aij Elements in the stiffness coefficient matrix are normalized for the density of the formation medium in the global coordinate system, and alpha is the P-wave phase velocity in the reference isotropic medium.
The step 5 comprises the following steps:
step 51, constructing an inversion determinant;
at step 52, an inversion determinant solution is performed.
In step 51, according to formulas (20) - (22), since there is only azimuth difference between local coordinate systems of the seismic lines distributed along different directions, A parameter ε under each local coordinate system z As in the global coordinate system, no further inversion is required; for the remaining five non-zero a parameters, the next inversion can be performed by constructing the following determinant; according to formulas (20) and (21), an inversion determinant is constructed as follows:
G 1 m 1 ＝d 1 , (24)
G 2 m 2 ＝d 2 , (25)
wherein ,G1 N x 3 coefficient matrix, N is the number of seismic lines distributed in different directions, matrix G is due to the 3 non-zero A parameters in equation (20) 1 The number of columns is 3; g 2 The number N of the rows is the number of the seismic lines distributed along different directions and the number of the columns is the number of non-zero A parameters in the formula (21) for the coefficient matrix of N multiplied by 2; matrix G 1 、G 2 The row vectors in (a) are respectively in the following forms:
vector m 1 、m 2 The forms of (a) are as follows:
m 1 ＝(ε x ，ε y ，η z ) T ， (28)
m 2 ＝(η x ，η y ) T ， (29)
vector d 1 、d 2 The forms of (a) are as follows:
in order to make the inverse problem of the formulas (24), (25) be an adaptive inverse problem, a coefficient matrix G is required 1 and G2 Is a positive or overdetermined matrix; therefore, the A parameter under the global coordinate system is obtained through the A parameter inversion under the local coordinate system where the plurality of azimuth seismic lines are positioned, and the seismic reflection wave travel time data of at least 3 azimuth are needed.
At step 52, equations (24) (25) can be solved by least squares, with the objective function of the inversion being:
||G 1 m 1 -d 1 || 2 ＜κ， (32)
||G 2 m 2 -d 2 || 2 ＜κ， (33)
wherein, κ is a parameter for controlling inversion accuracy; solving equations (32) (33) by equation (34):
wherein ,for inversion operators
wherein ,GT The inversion process is more stable with larger epsilon, but lower accuracy, which is the transpose of matrix G, I is N identity matrix, epsilon is a stability factor.
In step 6, by combining the data covariance matrix G d Conversion to model covariance matrix C m The accuracy of the calculated anisotropic parameters is evaluated:
C m ＝HC d H T ， (36)
here, theModel covariance matrix C m The probability of random distribution of the model parameter vector m is represented, and if the randomness does not exist, the covariance matrix is 0, and the model parameter vector m has no error. H T Is the transpose of matrix H.
In step 6, if the accurate model covariance matrix is calculated by:
C d ～σ 2 I， (37)
wherein I is an N x N identity matrix, σ passes χ 2 The residual error statistical method is used for calculating:
wherein ： the result of the calculation in equation (17) v is the difference between the number of rows and the number of columns of the matrix G.
The invention discloses a multi-azimuth reflected wave travel time inversion method of an orthotropic medium, which is a method for inverting the anisotropic parameters of the orthotropic medium in a global coordinate system according to the anisotropic parameters in different azimuth after inverting the anisotropic parameters of the orthotropic medium in a single azimuth through the reflected wave travel time in the azimuth aiming at the multi-azimuth reflected P wave travel time.
The invention has the advantage of providing a more reliable orthogonal anisotropic medium inversion method for providing more information. Dependence on priori information such as stratum thickness, vertical propagation speed and the like is reduced in the inversion process, and meanwhile, more anisotropic parameters can be obtained through inversion. Therefore, multidirectional seismic data can be more fully utilized, richer anisotropic information is provided, and a foundation is laid for subsequent stratum attribute identification and geological interpretation work. Geophysical data processing personnel can process multi-azimuth reflected wave travel time according to the method, or further develop a PSV wave inversion method according to the method provided by the invention.
Drawings
FIG. 1 is a schematic diagram of a reflected ray and global and local coordinate systems defined in the present invention;
FIG. 2 is a distribution range diagram of a seismic line in embodiment 1 of the invention;
FIG. 3 is a covariance matrix of the accuracy of the evaluated anisotropic parameters in example 1 of the present invention;
FIG. 4 is a graph showing the comparison of the anisotropy parameters and the accuracy values obtained by inversion in example 1 of the present invention;
FIG. 5 is a distribution range diagram of a seismic line in embodiment 2 of the invention;
FIG. 6 is a covariance matrix of the accuracy of the evaluated anisotropic parameters in example 2 of the present invention;
FIG. 7 is a graph comparing the anisotropy parameters obtained by inversion in example 2 of the present invention with the exact values;
FIG. 8 is a distribution range diagram of a seismic line in embodiment 3 of the invention;
FIG. 9 is a covariance matrix of the accuracy of the evaluated anisotropic parameters in example 3 of the present invention;
FIG. 10 is a graph showing the comparison of the anisotropy parameters and the accuracy values obtained by inversion in example 3 of the present invention;
FIG. 11 is a distribution range diagram of a seismic line in embodiment 4 of the invention;
FIG. 12 is a covariance matrix of the accuracy of the evaluated anisotropic parameters in example 4 of the present invention;
FIG. 13 is a graph showing the comparison of the anisotropy parameters and the accuracy values obtained by inversion in example 4 of the present invention;
FIG. 14 is a flow chart of a method for multi-azimuth reflected wave travel time inversion of an orthotropic medium according to the present invention.
Detailed Description
It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the invention. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of exemplary embodiments according to the present invention. As used herein, the singular forms also are intended to include the plural forms unless the context clearly indicates otherwise, and furthermore, it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, and/or combinations thereof.
As shown in fig. 14, fig. 14 is a flowchart of the orthogonal anisotropic medium multi-azimuth reflected wave travel time inversion method of the present invention. The orthogonal anisotropic medium multidirectional reflection wave travel time inversion method comprises the following steps:
step 1, establishing a global coordinate system and a local coordinate system;
first, assume a Cartesian coordinate system as the global coordinate system, x 3 The axis being vertical, x 1 ，x 2 The axes being horizontal and mutually orthogonal, the axial plane (x 1 ，x 2 )、(x 1 ，x 3 ) Respectively parallel to two symmetry planes of the medium. The background medium is uniformThe stratum thickness of the stratum is H, the horizontal reflecting surface at the bottom of the stratum is (x) 1 ，x 2 ) The planes are parallel. In this case, the incident downstream and reflected upstream rays of the P-wave lie in a plane perpendicular to the reflecting surface and are symmetrical with respect to the normal to the reflecting surface.
For a seismic observation system, a local coordinate system is defined. As shown in fig. 1, the reflected rays and two used coordinate systems are schematically represented: global coordinate system x i And a local coordinate system x' i . Corner angleIs the azimuth of the source detector profile, SO is the incident ray, and OR is the reflected ray.
The seismic wave is excited from a source S at the origin of the global coordinate system, reflected at point O, and propagates to a detector R. The axes on which the points S and R lie are defined as x 'of the local coordinate system' 1 Axis, and x' 1 The axes being in the same horizontal plane and being x' 1 The axis perpendicular to the axis is x' 2 An axis perpendicular to x' 1 Axis, x' 2 The axis of the shaft is x' 3 A shaft. The origin of the local coordinate system coincides with the source S and also represents the global coordinate system x i Origin of (x) vertical axis x 3 The same is true in both the local and global coordinate systems. The reflected rays lie in a local coordinate system (x' 1 ，x′ 3 ) In-plane, with a coordinate plane (x 1 ，x 3 ) Included angle
Step 2, establishing an orthotropic medium single-azimuth reflection P wave travel time approximate formula under a local coordinate system;
(1) Calculating basic formula during reflection travel
In a two-dimensional coordinate system, the reflected wave travel time T has the following form:
where x is the offset (distance between source S and detector R) and H is the depth of the horizontal reflecting surface (coincident with the plane of symmetry of the formation). T=t (x) denotes the travel time of the reflected P wave. v=v (n) denotes group velocity and n is a phase vector. The widely used representation method in time difference analysis is utilized:
wherein ,for normalized offset, α is the P-wave phase velocity in the reference isotropic medium, T 0 For a reference zero offset double pass. Equation (1) is rewritten as:
(2) Orthogonal anisotropic medium reflection travel time formula
Using phase velocity square approximation, i.e. v 2 (N)～c 2 (N) approximately represents group velocity v (N). In a two-dimensional coordinate system, the group velocity of an orthotropic medium can be expressed using an anisotropy parameter as:
in the formula (3), N is a velocity direction vector, which can be obtained byThe representation is made of a combination of a first and a second color,
the anisotropic parameters involved include epsilon x ，ε z ，η y, wherein ,εx ，ε z Respectively represent the medium in the coordinate axis x 1 、x 3 The difference between the direction P wave phase velocity and the reference velocity α; η (eta) y Representing the medium in a coordinate plane (x 1 ,x 3 ) Gradient of change in velocity of the internal P-wave. The anisotropic parameters in the local coordinate system are related to the stiffness coefficients in the local coordinate system:
wherein ,Aij Elements in the stiffness coefficient matrix are normalized for the density of the formation medium in the local coordinate system, and alpha is the P-wave phase velocity in the reference isotropic medium.
Simplified, equation (3) can be written in the form:
step 3, inversion of anisotropic parameters of the orthotropic medium based on the local coordinate system of single azimuth travel time;
(1) Epsilon calculation based on zero offset travel time z
At zero offset, i.e., x=0, equations (7) and (8) become:
therefore, the A parameter ε can be directly obtained by equation (12) z ：
(2) Construction of inversion determinant
According to equation (10), equations (7) and (8) can be rewritten as:
the inversion determinant is constructed according to equation (11) as follows:
Gm＝d, (12)
where G is a matrix of n×m coefficients, N is the number of detectors, M is the number of a parameters involved, m=2 in this section. The row vectors in matrix G are of the form:
m consists of 2 parameters, which are in the form:
m＝(ε x ，η y ) T ， (14)
the form of vector d is as follows:
for normalizing the offset.
(3) Inversion determinant solution
Equation (12) can be solved by a least squares method, and the inversion objective function is:
||Gm-d|| 2 ＜κ， (16)
wherein κ is a parameter controlling inversion accuracy. Solving equation (16) by equation (17):
wherein ,for inversion operators
wherein ,GT The inversion process is more stable with larger epsilon, but lower accuracy, which is the transpose of matrix G, I is N identity matrix, epsilon is a stability factor.
Step 4, establishing an anisotropic parameter conversion formula under a global coordinate system;
under a three-dimensional coordinate system, firstly, supposing that the seismic lines distributed along different directions on a plane, the trend angle of the lines isFrom the trend of the line x 1 The local coordinate system in the axial direction is converted into the global coordinate system, and the conversion matrix R is as follows:
we distinguish the orthotropic medium anisotropy parameters in the local coordinate system from the orthotropic medium anisotropy parameters in the global coordinate system using the superscript' ". According to the matrix transformation rule of 6 multiplied by 6 rigidity coefficient in Bond transformation, the anisotropic parameter epsilon 'of orthotropic medium in local coordinate system' x ，η′ y and ε′z The conversion to a global coordinate system can be achieved by the following formula:
ε′ z ＝ε z , (22)
the definition of the anisotropic parameters in the local coordinate system is shown in formula (6), and the global anisotropic parameters comprise epsilon x ，ε y ，ε z ，η x ，η y ，η z, wherein ,εx ，ε y ，ε z Respectively represent the medium in the coordinate axis x 1 、x 2 、x 3 The difference between the direction P wave phase velocity and the reference velocity α; η (eta) x ，η y ，η z Respectively representing the medium in a coordinate plane (x 2 ,x 3 )、(x 1 ,x 3 )、(x 1 ,x 2 ) Gradient of change in velocity of the internal P-wave. The anisotropic parameters in the global coordinate system are related to the stiffness coefficients in the global coordinate system:
wherein ,Aij Elements in the stiffness coefficient matrix are normalized for the density of the formation medium in the global coordinate system, and alpha is the P-wave phase velocity in the reference isotropic medium.
Step 5, carrying out global anisotropic parameter inversion based on a conversion formula;
(1) Construction of inversion determinant
According to formulas (20) to (22), since there is only a difference in azimuth angle between local coordinate systems in which the seismic lines distributed in different directions are located, the A parameter ε in each local coordinate system z As in the global coordinate system, no further inversion is required. For the remaining five non-zero a parameters, the next inversion can be performed by constructing the following determinant. According to formulas (20) and (21), an inversion determinant is constructed as follows:
G 1 m 1 ＝d 1 , (24)
G 2 m 2 ＝d 2 , (25)
wherein ,G1 N x 3 coefficient matrix, N is the number of seismic lines distributed in different directions, matrix G is due to the 3 non-zero A parameters in equation (20) 1 Is 3.G 2 For an n×2 coefficient matrix, the number of rows N is the number of seismic lines distributed in different directions, and the number of columns is the number of non-zero a parameters in equation (21). Matrix G 1 、G 2 The row vectors in (a) are respectively in the following forms:
vector m 1 、m 2 The forms of (a) are as follows:
m 1 ＝(ε x ，ε y ，η z ) T ， (28)
m 2 ＝(η x ，η y ) T ， (29)
vector d 1 、d 2 The forms of (a) are as follows:
in order to make the inverse problem of the formulas (24), (25) be an adaptive inverse problem, a coefficient matrix G is required 1 and G2 Is a positive or overdetermined matrix. Therefore, the A parameter under the global coordinate system is obtained through the A parameter inversion under the local coordinate system where the plurality of azimuth seismic lines are positioned, and the seismic reflection wave travel time data of at least 3 azimuth are needed.
(2) Inversion determinant solution
Equations (24) (25) can be solved by least squares, and the objective function of the inversion is:
||G 1 m 1 -d 1 || 2 ＜κ， (32)
||G 2 m 2 -d 2 || 2 ＜κ， (33)
wherein κ is a parameter controlling inversion accuracy. Solving equations (32) (33) by equation (34):
wherein ,for inversion operators
wherein ,GT The inversion process is more stable with larger epsilon, but lower accuracy, which is the transpose of matrix G, I is N identity matrix, epsilon is a stability factor.
And 6, performing inversion result precision evaluation.
By covariance matrix C of data d Conversion to model covariance matrix C m The accuracy of the calculated anisotropic parameters is evaluated:
C m ＝HC d H T ， (36)
here, theModel covariance matrix C m The probability of random distribution of the model parameter vector m is represented, and if the randomness does not exist, the covariance matrix is 0, and the model parameter vector m has no error.
If the accurate model covariance matrix is calculated by the following method:
C d ～σ 2 I， (37)
wherein I is an N x N identity matrix, σ passes χ 2 The residual error statistical method is used for calculating:
wherein ： the result of the calculation in equation (17) v is the difference between the number of rows and the number of columns of the matrix G.
The following are several embodiments of the invention
Example 1
In a specific embodiment 1 to which the present invention is applied, table 1 is a medium model parameter used in the numerical verification process of the present invention, the model comprising a set of 6 x 6 stiffness coefficient matrices, the matrices being symmetrical along diagonal elements, so that only the upper triangular matrix is shown.
Table 1 table of the anisotropy model and stiffness coefficient matrix used in example 1
Table 2 is an anisotropic parameter calculated by the anisotropic parameter formula in formula (23) based on the stiffness coefficient matrix provided in table 1 and the reference P-wave velocity, as an accurate value, compared with the anisotropic parameter obtained by inversion. The range of distribution of the data in this embodiment is also shown, wherein,the trend angle of the seismic line is shown, and x is the length of the seismic line.
TABLE 2 reference P-wave velocity and anisotropy parameter tables for the model in example 1
Fig. 2 is a distribution range of the seismic lines in example 1 plotted according to the data distribution range parameters in table 2, fig. 3 is a covariance matrix calculated according to formula (36) -formula (38), and fig. 4 is a comparison of the anisotropic parameters obtained by inversion with the accurate values in table 2, and the error bars are calculated according to the covariance matrix in fig. 3. The results of fig. 3 and fig. 4 prove that the anisotropic parameter inversion method of the orthotropic medium can obtain the anisotropic parameter of the medium more accurately.
Example 2
In a specific embodiment 2 to which the present invention is applied, table 3 is a medium model parameter used in the numerical verification process of the present invention, the model comprising a set of 6 x 6 stiffness coefficient matrices, the matrices being symmetrical along diagonal elements, so that only the upper triangular matrix is shown.
Table 3 table of anisotropy model and stiffness coefficient matrix used in example 2
Table 4 is an anisotropic parameter calculated by the anisotropic parameter formula in formula (23) based on the stiffness coefficient matrix provided in table 3 and the reference P-wave velocity, as an accurate value, compared with the anisotropic parameter obtained by inversion. The range of distribution of the data in this embodiment is also shown, wherein,the trend angle of the seismic line is shown, and x is the length of the seismic line.
TABLE 4 reference P-wave velocity and anisotropy parameter tables for the model in example 2
FIG. 5 is a plot of the distribution of the seismic lines of example 2 plotted against the data distribution parameters in Table 4, FIG. 6 is a covariance matrix calculated according to equation (36) -equation (38), and FIG. 7 is a comparison of the inverted anisotropy parameters with the exact values in Table 4, with the error bars calculated from the covariance matrix in FIG. 6. The results of fig. 6 and 7 can prove that when the distribution of the measuring lines is sparse and only four measuring lines are provided, the anisotropic parameter inversion method of the orthotropic medium can still obtain the anisotropic parameter of the medium more accurately.
Example 3
In a specific embodiment 3 to which the present invention is applied, table 5 is a medium model parameter used in the numerical verification process of the present invention, the model comprising a set of 6 x 6 stiffness coefficient matrices, the matrices being symmetrical along diagonal elements, so that only the upper triangular matrix is shown.
Table 5 table of anisotropy model and stiffness coefficient matrix used in example 3
Table 6 is an anisotropic parameter calculated by the anisotropic parameter formula in formula (23) based on the stiffness coefficient matrix provided in table 5 and the reference P-wave velocity, as an accurate value, compared with the anisotropic parameter obtained by inversion. The range of distribution of the data in this embodiment is also shown, wherein,the trend angle of the seismic line is shown, and x is the length of the seismic line.
TABLE 6 reference P-wave velocity and anisotropy parameter tables for the model in example 3
FIG. 8 is a plot of the distribution of the seismic lines of example 3 plotted against the data distribution parameters in Table 6, FIG. 9 is a covariance matrix calculated according to equation (36) -equation (38), and FIG. 10 is a comparison of the inverted anisotropy parameters with the exact values in Table 6, with the error bars calculated from the covariance matrix in FIG. 9. The results of fig. 9 and 10 prove that the anisotropic parameter inversion method of the orthotropic medium can still obtain the anisotropic parameter of the medium more accurately under the condition of only partial azimuth illumination.
Example 4
In a specific example 4 to which the present invention is applied, table 7 shows parameters of a media model used in the numerical verification process of the present invention, the model comprising a set of 6X 6 stiffness coefficient matrices, the matrices being symmetrical about diagonal elements, so that only the upper triangular matrix is shown.
Table 7 table of anisotropy model and stiffness coefficient matrix used in example 4
Table 8 is an anisotropic parameter calculated by the anisotropic parameter formula in formula (23) based on the stiffness coefficient matrix provided in table 7 and the reference P-wave velocity, as an accurate value, compared with the anisotropic parameter obtained by inversion. Meanwhile, the distribution range of the data in the embodiment is also shown, wherein phi is the trend angle of the seismic line, and x is the length of the seismic line.
TABLE 8 reference P-wave velocity and anisotropy parameter tables for the model in example 4
FIG. 11 is a plot of the distribution of the seismic lines of example 3 plotted against the data distribution parameters in Table 8, FIG. 12 is a covariance matrix calculated according to equation (36) -equation (38), and FIG. 13 is a comparison of the inverted anisotropy parameters with the exact values in Table 8, with the error bars calculated from the covariance matrix in FIG. 12. The results of fig. 12 and 13 can prove that the anisotropic parameter inversion method of the orthotropic medium can still obtain the anisotropic parameter of the medium more accurately under the condition of smaller maximum offset of the seismic lines.
Finally, it should be noted that: the foregoing description is only a preferred embodiment of the present invention, and is not intended to limit the present invention, but although the present invention has been described in detail with reference to the foregoing embodiment, it will be apparent to those skilled in the art that modifications may be made to the technical solution described in the foregoing embodiment, or equivalents may be substituted for some of the technical features thereof. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Other than the technical features described in the specification, all are known to those skilled in the art.
Claims (16)
1. The orthogonal anisotropic medium multidirectional reflection wave travel time inversion method is characterized by comprising the following steps of:
step 1, establishing a global coordinate system and a local coordinate system;
step 2, establishing an orthotropic medium single-azimuth reflection P wave travel time approximate formula under a local coordinate system;
step 3, carrying out anisotropic parameter inversion of the orthotropic medium based on the local coordinate system of single-azimuth travel time;
step 4, establishing an anisotropic parameter conversion formula under a global coordinate system;
step 5, carrying out global anisotropic parameter inversion based on a conversion formula;
and 6, performing inversion result precision evaluation.
2. The method for inversion of the travel time of an orthotropic medium multi-azimuth reflected wave according to claim 1, wherein in step 1, a Cartesian coordinate system is assumed as a global coordinate system, x thereof 3 The axis being vertical, x 1 ，x 2 The axes being horizontal and mutually orthogonal, the axial plane (x 1 ，x 2 )、(x 1 ，x 3 ) Respectively parallel to two symmetrical planes of the medium; the background medium is a uniform stratum, the thickness of the stratum is H, the horizontal reflecting surface at the bottom of the stratum and (x) 1 ，x 2 ) Planes are parallel; in this case, the incident downstream and reflected upstream rays of the P-wave lie in a plane perpendicular to the reflecting surface and are symmetrical with respect to the normal to the reflecting surface.
3. The method of inversion of the travel time of an orthotropic medium multidirectional reflected wave according to claim 2, wherein in step 1, for a seismic observation system, a local coordinate system, reflected rays and two used coordinate system diagrams are defined: global coordinate system x i And a local coordinate system x' i The method comprises the steps of carrying out a first treatment on the surface of the Corner angleIs the azimuth of the source detector profile, SO is the incident ray, and OR is the reflected ray.
4. The orthogonal anisotropic medium multidirectional reflected wave travel time inversion method according to claim 3, wherein in step 1, a seismic wave is excited from a seismic source S at the origin of a global coordinate system, reflected at a point O, and propagated to a detector R; the axes on which the points S and R lie are defined as x 'of the local coordinate system' 1 Axis, and x' 1 The axes being in the same horizontal plane and being x' 1 The axis perpendicular to the axis is x' 2 An axis perpendicular to x' 1 Axis, x' 2 The axis of the shaft is x' 3 A shaft; origin of local coordinate system and source SAnd also represents the global coordinate system x i Origin of (x) vertical axis x 3 The same is true in both local and global coordinate systems; the reflected rays lie in a local coordinate system (x' 1 ，x′ 3 ) In-plane, with a coordinate plane (x 1 ，x 3 ) Included angle
5. The orthotropic medium multi-azimuth reflected wave travel time inversion method according to claim 1, wherein in step 2, the reflected wave travel time T has the following form in a two-dimensional coordinate system:
wherein x is offset distance, namely distance between the seismic source S and the detector R, H is depth of the horizontal reflecting surface and coincides with the symmetry plane of the stratum; t=t (x) denotes the travel time of the reflected P wave; v=v (n) denotes group velocity, n being a phase vector; the widely used representation method in time difference analysis is utilized:
wherein ,for normalized offset, α is the P-wave phase velocity in the reference isotropic medium, T 0 Double-pass time-shifting for reference zero offset; equation (1) is rewritten as:
6. the method for inversion of the travel time of an orthotropic medium multidirectional reflection wave according to claim 5, wherein in step 2, a phase velocity square approximation, v, is adopted 2 (N)～c 2 (N) approximately represents group velocity v (N); in a two-dimensional coordinate system, the group velocity of an orthotropic medium can be expressed using an anisotropy parameter as:
in the formula (3), N is a velocity direction vector, which can be obtained byThe representation is made of a combination of a first and a second color,
the anisotropic parameters involved include epsilon x ，ε z ，η y, wherein ,εx ，ε z Respectively represent the medium in the coordinate axis x 1 、x 3 The difference between the direction P wave phase velocity and the reference velocity α; η (eta) y Representing the medium in a coordinate plane (x 1 ,x 3 ) A gradient of change in velocity of the internal P-wave; the anisotropic parameters in the local coordinate system are related to the stiffness coefficients in the local coordinate system:
wherein ,Aij Normalizing elements in the stiffness coefficient matrix for the density of the stratum medium under a local coordinate system, wherein alpha is the P wave phase speed in the reference isotropic medium;
simplified, equation (3) can be written in the form:
7. the orthotropic medium multi-azimuth reflected wave travel time reversal method according to claim 6, wherein step 3 includes:
step 31, calculating ε based on zero offset travel time z ；
Step 32, constructing an inversion determinant;
step 33, solving the inversion determinant.
8. The orthotropic medium multi-azimuth reflected wave travel time inversion method according to claim 7, wherein at step 31, at zero offset, x=0, formula (7) and formula (8) become:
therefore, the A parameter ε can be directly obtained by equation (12) z ：
9. The orthotropic medium multi-azimuth reflected wave travel time inversion method according to claim 8, wherein in step 32, according to formula (10), formula (7) and formula (8) are rewritten as:
the inversion determinant is constructed according to equation (11) as follows:
Gm＝d, (12)
wherein G is a coefficient matrix of n×m, N is the number of detectors, M is the number of a parameters involved, m=2 in this section; the row vectors in matrix G are of the form:
m consists of 2 parameters, which are in the form:
m＝(ε x ，η y ) T ， (14)
the form of vector d is as follows:
to normalize offset, T obs For the travel time received by the detector.
10. The orthotropic medium multi-azimuth reflected wave travel time inversion method of claim 9, wherein in step 33, the equation (12) can be solved by a least squares method, and the inversion objective function is:
||Gm-d|| 2 ＜κ， (16)
wherein, κ is a parameter for controlling inversion accuracy; solving equation (16) by equation (17):
wherein ,for inversion operators
wherein ,GT The inversion process is more stable with larger epsilon, but lower accuracy, which is the transpose of matrix G, I is N identity matrix, epsilon is a stability factor.
11. The method for multi-azimuth reflected wave travel-time inversion of orthotropic medium according to claim 10, wherein in step 4, under three-dimensional coordinate system, firstly, it is assumed that seismic lines are distributed along different directions on a plane, and the travel angle of the lines isFrom the trend of the line x 1 The local coordinate system in the axial direction is converted into the global coordinate system, and the conversion matrix R is as follows:
distinguishing the orthotropic medium anisotropy parameters in the local coordinate system from the orthotropic medium anisotropy parameters in the global coordinate system using a superscript; according to the matrix transformation rule of 6 multiplied by 6 rigidity coefficient in Bond transformation, the anisotropic parameter epsilon 'of orthotropic medium in local coordinate system' x ，η′ y and ε′z The conversion to a global coordinate system can be achieved by the following formula:
ε′ z ＝ε z , (22)
the definition of the anisotropic parameters in the local coordinate system is shown in formula (6), and the global anisotropic parameters comprise epsilon x ，ε y ，ε z ，η x ，η y ，η z, wherein ,εx ，ε y ，ε z Respectively represent the medium in the coordinate axis x 1 、x 2 、x 3 The difference between the direction P wave phase velocity and the reference velocity α; η (eta) x ，η y ，η z Respectively representing the medium in a coordinate plane (x 2 ,x 3 )、(x 1 ,x 3 )、(x 1 ,x 2 ) A gradient of change in velocity of the internal P-wave; the anisotropic parameters in the global coordinate system are related to the stiffness coefficients in the global coordinate system:
wherein ,Aij Elements in the stiffness coefficient matrix are normalized for the density of the formation medium in the global coordinate system, and alpha is the P-wave phase velocity in the reference isotropic medium.
12. The orthotropic medium multi-azimuth reflected wave travel time reversal method according to claim 11, wherein step 5 includes:
step 51, constructing an inversion determinant;
at step 52, an inversion determinant solution is performed.
13. The method of inversion of the travel time of an orthotropic medium multi-azimuth reflected wave according to claim 12, wherein in step 51, according to formulas (20) to (22), only the seismic lines distributed along different directions exist between the local coordinate systemsAzimuth angle difference, thus A parameter epsilon under each local coordinate system z As in the global coordinate system, no further inversion is required; for the remaining five non-zero a parameters, the next inversion can be performed by constructing the following determinant; according to formulas (20) and (21), an inversion determinant is constructed as follows:
G 1 m 1 ＝d 1 , (24)
G 2 m 2 ＝d 2 , (25)
wherein ,G1 N x 3 coefficient matrix, N is the number of seismic lines distributed in different directions, matrix G is due to the 3 non-zero A parameters in equation (20) 1 The number of columns is 3; g 2 The number N of the rows is the number of the seismic lines distributed along different directions and the number of the columns is the number of non-zero A parameters in the formula (21) for the coefficient matrix of N multiplied by 2; matrix G 1 、G 2 The row vectors in (a) are respectively in the following forms:
vector m 1 、m 2 The forms of (a) are as follows:
m 1 ＝(ε x ，ε y ，η z ) T ， (28)
m 2 ＝(η x ，η y ) T ， (29)
vector d 1 、d 2 The forms of (a) are as follows:
in order to make the inverse problem of the formulas (24), (25) be an adaptive inverse problem, a coefficient matrix G is required 1 and G2 Is a positive or overdetermined matrix; therefore, the A parameter under the global coordinate system is obtained through the A parameter inversion under the local coordinate system where the plurality of azimuth seismic lines are positioned, and the seismic reflection wave travel time data of at least 3 azimuth are needed.
14. The orthotropic medium multi-azimuth reflected wave travel time inversion method according to claim 13, wherein in step 52, formulas (24) (25) can be solved by least squares method, and the inversion objective function is:
||G 1 m 1 -d 1 || 2 ＜κ， (32)
||G 2 m 2 -d 2 || 2 ＜κ， (33)
wherein, κ is a parameter for controlling inversion accuracy; solving equations (32) (33) by equation (34):
wherein ,for inversion operators
wherein ,GT The inversion process is more stable with larger epsilon, but lower accuracy, which is the transpose of matrix G, I is N identity matrix, epsilon is a stability factor.
15. The method of orthogonal anisotropic media multi-azimuth reflected wave travel time inversion according to claim 14, wherein in step 6, the data covariance matrix C is obtained by d Conversion to model covariance matrix C m The accuracy of the calculated anisotropic parameters is evaluated:
C m ＝HC d H T ， (36)
here, theModel covariance matrix C m Representing the probability of random distribution of the model parameter vector m, if the randomness does not exist, the covariance matrix is 0, and the model parameter vector m has no error at the moment, H T Is the transpose of matrix H.
16. The orthotropic medium multi-azimuth reflected wave travel time inversion method according to claim 15, wherein in step 6, if an accurate model covariance matrix is calculated by:
C d ～σ 2 I， (37)
wherein I is an N x N identity matrix, σ passes χ 2 The residual error statistical method is used for calculating:
wherein ： the result of the calculation in equation (17) v is the difference between the number of rows and the number of columns of the matrix G.
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